The MBP preservation recently has also attracted increasingly attention in the field of numerical methods for the Allen–Cahn type equations of the form (REF ).
The semi-implicit schemes were extensively studied in,
e.g. [1]}, [2]}, [3]}, [4]}, [5]}, [6]},
for the classic, fractional, or surface Allen–Cahn equations.
The first- and second-order stabilized ETD schemes were shown to
preserve the MBP unconditionally for the nonlocal Allen–Cahn equation [7]}
and the conservative Allen–Cahn equation [8]}.
An abstract framework on MBP preservation of the ETD schemes
for a class of semilinear parabolic equations was established in [9]},
where sufficient conditions for the linear and nonlinear operators are presented in order to guarantee the MBP.
A family of stabilized integrating factor Runge-Kutta (IFRK) schemes, up to third order, were developed in [10]}, which can
unconditionally preserve the MBP. In addition, a fourth-order (conditionally) MBP-preserving IFRK scheme was presented in [11]}.
So far, as one of the very popular methods, there is still not much systematical study on MBP-preserving SAV schemes.
